Question

An object is allowed to fall from a height $R$ above the earth, where $R$ is the radius of earth Its velocity when it strikes the earth's surface, ignoring air resistance, will be

• A. $\sqrt{g R}$
• B. $2 \sqrt{g R}$
• C. $\sqrt{2 g R}$
• D. $\sqrt{\frac{g R}{2}}$

Answer 1

The Correct Option is A

The correct answer is (A) : $\sqrt{g R}$
Loss in PE = Gain in KE
$\left(-\frac{GMm}{2R}\right)-\left(-\frac{GMm}{R}\right)=\frac{1}{2}m{v}^2$
$\Rightarrow v^2=\frac{GM}{R}=gR$
$\Rightarrow v=\sqrt{gR}$